Introduction

There have been a variety of techniques applied to the restoration of HST images over the last several years (White 1991, Weir 1991). Most of these approaches have concentrated on algorithms already developed and well accepted by those in the astronomical community. At the same time, however, the signal and image processing community was developing a number of digital image restoration techniques which were motivated largely by non-astronomical problems (Andrews and Hunt 1977). For a recent review and classification of image restoration algorithms, see Katsaggelos (1991). For the most part, the algorithms introduced by image processing scientists tend to be very general and applicable to a variety of imaging problems. In examining the HST degraded images, it is apparent that many of the image restoration techniques, and in particular the iterative techniques, developed in the realm of signal and image processing would be well suited for application to this special problem.

In this paper two iterative image restoration techniques are applied to the HST data restoration problem. These are the generalized iterative adaptive algorithm (Kang and Katsaggelos 1993) and the frequency domain iterative adaptive algorithm (Kang and Katsaggelos 1992). Both are based on a set-theoretic approach to image restoration. The critical factor in choosing these algorithms is that, unlike many regularized restoration techniques, these algorithms need no prior information about the signal and no knowledge of the noise variances present. These are also relatively fast algorithms, and have been developed with convergence speed as a consideration. The generalized iterative adaptive algorithm allows for spatial adaptivity and is applicable to the case of spatially variant degradation.

The performance of these algorithms is very good with the HST data that we have tested. The criteria which are most important to the astronomical community have been utilized in compiling the results here. It can be seen from these results that there is much potential for use of these iterative constrained least squares algorithms from the viewpoint of not only quality of results, but also convergence speed. In the next section, we describe the fundamentals of set theoretic image restoration, and describe the iterative techniques that we have developed through this approach.